The special theory of relativity describes the motion and dynamics of objects moving at significant fractions of the speed of light.

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Is proper time and proper length relative or absolute in relation to two events?

This question concerns with a problem encountered when doing a question on special relativity. A scenario in which the question is based will be described and the problem will be explained. Scenario: ...
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Point charge 4-current derivation

How do I derive that the 4-current of a point charge is $$j^{\mu}(x)=e\int_{-\infty}^{+\infty}\dot{z}^{\mu}(s)\delta^4(x-z(s))ds$$ where $\dot{z}^{\mu}(s)$ is the 4-velocity of the charge and $s$ is ...
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Fierz identity for chiral fermions [closed]

First of all I define the convention I use. The matrices $\bar{\sigma}^\mu$ I will use are $\{ Id, \sigma^i \}$ where $\sigma^i$ are the Pauli matrices and $Id$ is the 2x2 identity matrix. I will use ...
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Applications of octonions in special relativity?

According to the Wikipedia article on octonions: Octonions [...] have applications in fields such as string theory, special relativity, and quantum logic. However, I couldn't find any ...
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Composition of Lorentz Transformations

If a particle is moving in the $x$-direction with velocity $c/2$, then the Lorentz transformation $\Lambda = \begin{pmatrix}\gamma & -\beta \gamma & 0 & 0 \\ -\beta \gamma & \gamma ...
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What particles travel near the speed of a photon? [closed]

I know photons travel at the speed of light. How does the size of a particle determine its maximum velocity? Phonons, Preons, Electron ect. Is there a scale in from the smallest particle's maximum ...
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90 views

Why does Special Relativity apply to more than just light?

It is my understanding that time dilation is derived from the constancy of the speed of light in vacuum. I would assume this implies that the quirky consequences would therefore apply only to light. ...
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Is the time dilation experiment for real?

A popular experiment is described in books on special relativity, that claims that an atomic clock was flown at high speed and later compared with a similar atomic clock on earth, and it was found ...
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Pole and Barn Paradox w/ Spacetime Interval

I'm having trouble with a pole and barn paradox problem. The problem is as follows: A pole vaulter is running with a pole at $ v=\frac{\sqrt3}{2}c $. Her pole has a proper length of $L$. She runs ...
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Relativistic Mass and Potential Energy

In the chapter 16–4 of the Feynman Lectures, Feynman employs a thought experiment to explain why "if two particles come together and produce potential or any other form of energy; if the pieces are ...
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4answers
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Am I just some energy traveled at light speed? [closed]

I don't understand $E=mc^2$ very well, and here is my question: Does this equation mean masses are just condensed energy? And does this mean that the extra energy an object has when traveling at ...
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1answer
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Proving that interval preserving transformations are linear

In almost all proofs I've seen of the Lorentz transformations one starts on the assumption that the required transformations are linear. I'm wondering if there is a way to prove the linearity: Prove ...
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Einsteins theory of relativity and formula of kinetic energy [duplicate]

After seeing both Einstein's theory of relativity ($E=mc^2$) and the formula of kinetic energy (K.E=$\frac{mv^2}{2}$), I noticed that that they are mostly the same, with the only difference that ...
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0answers
39 views

Is the helicity of photon Lorentz invariant? [closed]

If the helicity of a photon is $+1$ in an inertial frame, then is the helicity of this photon $+1$ in another inertial frame? The helicity operator is $$ h=\mathbf{S}\cdot\hat{\mathbf{p}} $$ with $$ ...
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1answer
75 views

Where is the mistake in the following rationament [duplicate]

Well... kind of hard to translate in English so bare with me :). Let's consider a wheel that spins in the void. Each point of the wheel has the speed $v = ω r$. That means that for any $ω$, there is ...
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2answers
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Nature of light in Special Relativity

What is the nature of light in the context of Special Relativity? Is it a photon, or an electromagnetic wave, or something else? I have doubts, because a photon seems to me a quantum mechanical ...
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6answers
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Relativistic Cellular Automata

Cellular automata provide interesting models of physics: Google Scholar gives more than 25,000 results when searching for "cellular automata" physics. Google Scholar still gives more than 2.000 ...
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Relativistic Doppler effect derivation

This is about a step in a derivation of the expression for the relativistic Doppler effect. Consider a source receding from an observer at a velocity $v$ along the line joining the two. Light is ...
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3answers
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How do Doppler Effect and Time Dilation differ?

Above, I have drawn a diagram showing Doppler Effect (here we are using space-time but in a non-relativistic sense. Time and distance are the same for A and B). Edit: I am adding a relativistic ...
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2answers
66 views

Is time a coordinate or a parameter in Newtonian mechanics?

In classical (Newtonian) mechanics we only ever seem to consider 3-dimensional space, with physical quantities being represented by 3-vectors. My understanding for this is because in classical ...
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1answer
2k views

4-momentum of photon

The 4-momentum is defined as $p=mU$ where m is the rest mass of the particle and $U$ is the 4-velocity. Now I am confused as to how this applies to a photon for which one can't define $U$ since there ...
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2answers
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Motivation for usage of 4-vectors in special relativity

I understand that if one considers a 4-dimensional space-time from the outset then 4-vectors are the natural quantities to consider (as opposed to 3-vectors as in Newtonian mechanics), since the ...
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1answer
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Time-reversed twin paradox

This started with wondering about the nature of certain physical quantities under time-reversal - chiefly, that acceleration retains its magnitude and direction at a given time regardless of the ...
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Relativistic correction to Hydrogen atom - Perturbation theory

Given the relativistic correction $$ H_1' = - \frac{p^4}{8m^3 c^2} $$ to the Hamiltonian (i.e. a perturbation), what does it mean when $[H_1', \mathbf{L}] = 0$? The book I'm reading says this implies ...
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2answers
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Is acceleration relative in relativity?

Suppose a box A is moving relative to a Box B, then by time dilation equation if I take 1 sec passed for an observer in A then for an observer in B will be little longer. Now if I suppose that the box ...
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Galileo's ship experiment with a laser pen instead of a rock

Ship's mast experiment with the boat moving at speed v: If a rock is dropped from the mast, then for an observer inside the boat they will see this: For an observer outside the boat and on the ...
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Momentum equation of a beam hitting a stationary target to create antiprotons

I'm struggling with the solution of a physics exercise which is to calculate the minimum energy needed to create antiprotons when a proton beam scatters on a stationary proton target: $$p + p ...
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Definition of the Lorentz transformations [closed]

Until very recently I believed that the Lorentz transformations were defined as "the transformations that carry one inertial reference frame into another". In Wikipedia's page we find something along ...
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1answer
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Homogeneity and isotropy and derivation of the Lorentz transformations

In deriving the Lorentz transformations I have found (from reading a few different sets lecture notes) that it is argued that they must be linear and thus there general form must be $$x'=Ax+Bt,\quad ...
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Zeroth component of 4-momentum and relativistic energy-momentum relation

As I understand it one is forced to use 4-vectors since we require objects that transform as vectors under application of Lorentz transformations and 3-vectors do not (technically they do under ...
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Speed of the Coulomb Field Measured To Be “Infinite”

The paper "Measuring Propagation Speed of Coulomb Fields" by R. de Sangro et al points out that: ...the Lienard-Weichert retarded potential leads to the same formula as the one obtained assuming ...
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Inertial coordinate systems [duplicate]

In Newtonian mechanics, by the following two assumptions: (i) The time is absolute. (ii) The length is absolute. it is easy find the relations betweem two coordinate systems with uniform motion ...
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Path integral (sum over paths where $v>c$) [closed]

The path integral formalism is used to get for example the propagator of particles. In this formalism we integrate over all mathematically possible paths (and weight them with the non-relativistic ...
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2answers
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How do we determine if a certain physical quantity is a vector?

For instance in Newtonian physics we treat position of objects, displacements, velocities, forces, momenta, angular velocities etc all as vector quantities (little arrows in space which have a certain ...
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Frames of reference, relativity, and a ball thrown in the air

Ever since my high school physics days I found relativity fascinating but I don't think I have great insight even into special relativity. For example, in almost every lesson or video they give an ...
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1answer
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What is really sought when we purpose Einstein's postulates in Special Relativity?

Special Relativity can be motivated by looking at Maxwell's Electrodynamics and noticing that there is some kind of inconsistency between it and Newtonian Mechanics. Indeed, as Einstein pointed out on ...
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Deriving the speed of the propagation of a change in the Electromagnetic Field from Maxwell's Equations

I've been told that, from Maxwell's equations, one can find that the propagation of change in the Electromagnetic Field travels at a speed $\frac{1}{\sqrt{\mu_0 \epsilon_0}}$ (the values of which can ...
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Exact definition of momentarily comoving reference frame (MCRF)

Consider a particle $P$ in the framework of special relativity with position $r(t)=(ct,x(t),y(t),z(t))$ respect to an inertial reference frame $\Sigma=(ct,x,y,z;O)$. I need to know if the following ...
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1answer
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Questions about null geodesic [closed]

Show for the null geodesic in 3D flat spacetime using polar coordinates so the line element is $ds^2=-dt^2+dr^2+r^2d\phi^2$. Do light rays move on straight lines? My question is that I only learned ...
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1answer
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How to motivate the importance of the spacetime interval

The spacetime interval is a rather important thing in Special Relativity. It allows us to define the separation between any two events as spacelike, timelike or lightlike and more importantly, the ...
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What if a faster-than-light particle is found?

What will be the consequence (severe ones) on laws of physics if a particle that travels faster than light is discovered? I am looking for a more general answer so that a high school student would be ...
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2answers
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Relativity gedanken experiment

Lets consider the following thought experiment: A spaceship is in circular orbit around Earth traveling at 99% of $c$ (the orbital distance is chosen in such a way that inside the ship there are no ...
3
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1answer
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Limits used to find non-rel limit of the Klein-Gordon equation

I just have a question regarding assessing the non-relativistic limit of the Klein-Gordon equation. In the book I'm following (Quantum Mechanics by Bransden & Joachain) they use the limits (Chpt. ...
6
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1answer
237 views

Lorentz invariance, energy-momentum conservation & the locality of interactions

I have been reading these notes ("Minkowski Spacetime: A Hundred Years Later", by Vesselin Petkov) 1, in which the author states (in the middle of the text on page 137) that "The only Lorentz ...
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Does contracted spring weigh more than stretched one?

(One of examples that potential energy contributes to mass.) Does hot object weigh more than cold one? (One of examples that kinetic energy contributes to mass.) If these are true and justified by ...
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2answers
109 views

What is the inconsistency between Maxwell's electrodynamics and newtonian mechanics?

As far as I understand, when a modification of a theory is made it is because some observation required this modifcation. Quantum Mechanics is a nice example of that: observations of microscopic ...
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2answers
509 views

Why doesn't the existence of proper-time $\tau$ imply a preferred reference frame?

A proper time interval $\Delta\tau$ for a given observer is a relativistic invariant. However, the calculation of $\Delta\tau$ requires reference to some arbitrary coordinate time t: $$\Delta\tau = ...
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Question/Doubt about Time Dilation Symmetry in Special Relativity

Apologies if this has been asked and answered before, as I am still having doubts reconciling the symmetrical effects of time dilation (i.e each frame sees clocks of other frame slowing down), and I ...
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Relativity of simultaneity: Is my reasoning here correct?

I have a situation similar to that underlying the twin 'paradox' - the observer m1 below remains stationary while the observer m2 goes off on a space-time trajectory, and then returns to m1's ...